Fully online classification by regularization

Applied and Computational Harmonic Analysis

Volumn 23, Issue 2, 2007, Pages 198-214

  Ye, Gui Bo ^a   Zhou, Ding Xuan ^b  

^a FUDAN UNIVERSITY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Classification algorithm; Error analysis; Online learning; Regularization; Reproducing kernel Hilbert spaces

Indexed keywords

ALGORITHMS; CLASSIFICATION (OF INFORMATION); ERROR ANALYSIS; PARAMETER ESTIMATION; SUPPORT VECTOR MACHINES;

CLASSIFICATION ALGORITHM; ONLINE LEARNING; REPRODUCING KERNEL HILBERT SPACES;

ONLINE SYSTEMS;

EID: 34547603945     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2006.12.001     Document Type: Article

References (27)

1. Aronszajn N. Theory of reproducing kernels. Trans. Amer. Math. Soc. 68 (1950) 337-404
2. Bartlett P.L., Jordan M.I., and McAuliffe J.D. Convexity, classification, and risk bounds. J. Amer. Statist. Assoc. 101 (2006) 138-156
3. Chen D.R., Wu Q., Ying Y., and Zhou D.X. Support vector machine soft margin classifiers: Error analysis. J. Mach. Learn. Res. 5 (2004) 1143-1175
4. Cesa-Bianchi N., Long P., and Warmuth M.K. Worst-case quadratic loss bounds for prediction using linear functions and gradient descent. IEEE Trans. Neural Networks 7 (1996) 604-619
5. Cesa-Bianchi N., Conconi A., and Gentile C. On the generalization ability of on-line learning algorithms. IEEE Trans. Inform. Theory 50 (2004) 2050-2057
6. De Vito E., Caponnetto A., and Rosasco L. Model selection for regularized least-squares algorithm in learning theory. Found. Comput. Math. 5 (2005) 59-85
7. Devroye L., Györfi L., and Lugosi G. A Probabilistic Theory of Pattern Recognition (1997), Springer-Verlag, New York
8. Evgeniou T., Pontil M., and Poggio T. Regularization networks and support vector machines. Adv. Comput. Math. 13 (2000) 1-50
9. Forster J., and Warmuth M.K. Relative expected instantaneous loss bounds. J. Comput. Syst. Sci. 64 (2002) 76-102
10. Kivinen J., Smola A.J., and Williamson R.C. Online learning with kernels. IEEE Trans. Signal Process. 52 (2004) 2165-2176
11. Lin Y. Support vector machines and the Bayes rule in classification. Data Min. Knowl. Discov. 6 (2002) 259-275
12. Lugosi G., and Vayatis N. On the Bayes-risk consistency of regularized boosting methods. Ann. Statist. 32 (2004) 30-55
13. Mukherjee S., Rifkin R., and Poggio T. Regression and classification with regularization. In: Denison D.D., Hansen M.H., Holmes C., Mallick B., and Yu B. (Eds). Nonlinear Estimation and Classification (2002), Springer-Verlag, New York 107-124
14. Rakhlin A., Mukherjee S., and Poggio T. Stability results in learning theory. Anal. Appl. 3 (2005) 397-417
15. Rosenblatt F. Principles of Neurodynamics (1962), Spartan Book, New York
16. C. Scovel, I. Steinwart, Fast rates for support vector machines, in: Proc. 18th Conf. on Learning Theory (COLT-2005), Bertinoro, Italy, 2005
17. Smale S., and Yao Y. Online learning algorithms. Found. Comput. Math. 6 (2006) 145-170
18. Smale S., and Zhou D.X. Estimating the approximation error in learning theory. Anal. Appl. 1 (2003) 17-41
19. Smale S., and Zhou D.X. Shannon sampling and function reconstruction from point values. Bull. Amer. Math. Soc. 41 (2004) 279-305
20. Smale S., and Zhou D.X. Shannon sampling II: Connections to learning theory. Appl. Comput. Harmon. Anal. 19 (2005) 285-302
21. S. Smale, D.X. Zhou, Learning theory estimates via integral operators and their applications, Constr. Approx., in press
22. Steinwart I. Support vector machines are universally consistent. J. Complexity 18 (2002) 768-791
23. P. Tarrès, Y. Yao, Online learning as stochastic approximations of regularization paths, preprint, 2005
24. Wahba G. Spline Models for Observational Data (1990), SIAM, Philadelphia
25. Q. Wu, Y. Ying, D.X. Zhou, Multi-kernel regularized classifiers, J. Complexity, in press
26. Ying Y., and Zhou D.X. Online regularized classification algorithms. IEEE Trans. Inform. Theory 52 (2006) 4775-4788
27. Zhang T. Statistical behavior and consistency of classification methods based on convex risk minimization. Ann. Statist. 32 (2004) 56-85